<h2>Problem 102</h2>
<div style="color:#666;font-size:80%;">12 August 2005</div><br />
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<p>Three distinct points are plotted at random on a Cartesian plane, for which -1000 <img src='images/symbol_le.gif' width='10' height='12' alt='&le;' border='0' style='vertical-align:middle;' /> <i>x</i>, <i>y</i> <img src='images/symbol_le.gif' width='10' height='12' alt='&le;' border='0' style='vertical-align:middle;' /> 1000, such that a triangle is formed.</p>
<p>Consider the following two triangles:</p>
<p style='text-align:center;'>A(-340,495), B(-153,-910), C(835,-947)<br /><br />
X(-175,41), Y(-421,-714), Z(574,-645)</p>
<p>It can be verified that triangle ABC contains the origin, whereas triangle XYZ does not.</p>
<p>Using <a href='project/triangles.txt'>triangles.txt</a> (right click and 'Save Link/Target As...'), a 27K text file containing the co-ordinates of one thousand &quot;random&quot; triangles, find the number of triangles for which the interior contains the origin.</p>
<p class='info'>NOTE: The first two examples in the file represent the triangles in the example given above.</p>

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